Explain why the value of \(k\) gets larger as the temperature of a reaction mixture is increased.

The study of chemical kinetics involves understanding how reaction rates are influenced by various factors and the mechanisms by which reactions occur. One of the fundamental aspects in this field is the rate at which reactants turn into products. Reaction rates can vary greatly, from fractions of a second to years, depending on the system and conditions.

A key equation in chemical kinetics is the Arrhenius equation, which shows the dependency of the reaction rate on temperature and activation energy. Knowing this equation allows chemists to predict how changing the conditions may affect the speed of a chemical reaction, which is vital for processes ranging from industrial synthesis to biological metabolism.

The rate constant, symbolized by the letter 'k', is a proportionality factor that is specific to each chemical reaction. It plays a critical role in the kinetics of a reaction, linking the rate of reaction to the concentration of the reactants raised to a power, typically corresponding to the reaction order.

In the Arrhenius equation, the rate constant reflects how even a small change in temperature can lead to a significant change in the reaction rate. The value of 'k' is crucial for calculating reaction rates and designing chemical processes, as it determines the speed at which products are formed.

The concept of activation energy, denoted as 'Ea', is central to understanding how chemical reactions occur. It represents the minimum energy that reacting particles must have for a reaction to take place. Activation energy can be thought of as a barrier that reactants must overcome to transform into products.

In the Arrhenius equation, a higher activation energy means a slower reaction rate, as fewer reactant molecules will have the energy required to surpass this barrier. Conversely, when activation energy is low, more particles have the needed energy, thus increasing the rate at which reactants are converted into products.

Temperature is a measure of the kinetic energy of particles, and it has a profound effect on the rate of chemical reactions, as articulated in the Arrhenius equation. Raising the temperature of a reaction increases the energy of the particles, which in turn increases the number of collisions with energy equal to or greater than the activation energy.

This increase in collision frequency and energy means that more reactant particles can overcome the activation energy barrier per unit time, leading to an increase in the reaction rate. Consequently, understanding the influence of temperature on reaction kinetics is critical for controlling the conditions under which chemical reactions are carried out.